Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An efficient numerical method based on an H1–gradient projection method is introduced and finally several numerical results demonstrate the applicability of the approach.
CITATION STYLE
Blank, L., Farshbaf-Shaker, M. H., Garcke, H., Rupprecht, C., & Styles, V. (2014). Multi-material phase field approach to structural topology optimization. In International Series of Numerical Mathematics (Vol. 165, pp. 231–246). Springer. https://doi.org/10.1007/978-3-319-05083-6_15
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